To calculate the maximum data rate (Mbps) of an optical fiber, we can use a simplified approach that assumes the fiber is operating at its theoretical maximum capacity. The Maximum Bit Rate (B) in megabits per second (Mbps) for a fiber optic cable is approximately determined by the Bandwidth-Delay Product:

$B \approx \frac{c}{L \times n_{\text{avg}}}$

Where:

• $B$ is the maximum bit rate in bits per second.
• $c$ is the speed of light in vacuum ($3 \times 10^8 \, \text{m/s}$).
• $L$ is the length of the fiber in meters.
• $n_{\text{avg}}$ is the average refractive index of the core and cladding.

To solve the problem step by step:

1. Convert fiber length into meters:
   $L = 13 \, \text{km} = 13,000 \, \text{m}$

2. Calculate the average refractive index ($n_{\text{avg}}$):
   The refractive indices of the core and cladding are given as: $n_1 = 1.47 \quad \text{(core)}, \quad n_2 = 1.45 \quad \text{(cladding)}$ $n_{\text{avg}} = \frac{n_1 + n_2}{2} = \frac{1.47 + 1.45}{2} = 1.46$

3. Calculate the delay: The delay is essentially the time it takes for light to travel through the fiber, which can be calculated as: $\text{Delay} = \frac{L}{c/n_{\text{avg}}} = \frac{13,000}{3 \times 10^8 / 1.46} = \frac{13,000}{2.054 \times 10^8} \, \text{seconds}$ Let's compute this step.

The delay for light to travel through the fiber is approximately $6.33 \times 10^{-5}$ seconds.

4. Estimate the maximum bit rate:
   The Maximum Bit Rate (B) is inversely proportional to the delay, so we can use the following relation: $B = \frac{1}{\text{Delay}} \, \text{bits per second}$ Let's calculate this.

It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to continue with another query or clarification? Below are some related questions you might find useful:

1. How does the refractive index affect data transmission in optical fibers?
2. What are the differences between multimode and single-mode fibers?
3. How does dispersion affect the performance of an optical fiber?
4. What factors limit the maximum data rate in fiber optic communications?
5. How does wavelength division multiplexing (WDM) increase the capacity of fiber optics?

Tip: Always account for both core and cladding refractive indices when estimating the average refractive index for fiber optics.